\[ \left (x^2+y(x)^2\right ) f\left (\frac {x}{\sqrt {x^2+y(x)^2}}\right ) \left (y'(x)^2+1\right )-\left (x y'(x)-y(x)\right )^2=0 \] ✓ Mathematica : cpu = 3.94272 (sec), leaf count = 229
\[\left \{\text {Solve}\left [c_1=\log (x)+\int _1^{\frac {y(x)}{x}} \frac {\left (K[1]^2+1\right ) f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )-1}{(K[1]-i) (K[1]+i) \sqrt {f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )} \left (K[1] \sqrt {f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )}+i \sqrt {f\left (\frac {1}{\sqrt {K[1]^2+1}}\right )-1}\right )} \, dK[1],y(x)\right ],\text {Solve}\left [c_1=\log (x)+\int _1^{\frac {y(x)}{x}} \frac {\left (K[2]^2+1\right ) f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )-1}{(K[2]-i) (K[2]+i) \sqrt {f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )} \left (K[2] \sqrt {f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )}-i \sqrt {f\left (\frac {1}{\sqrt {K[2]^2+1}}\right )-1}\right )} \, dK[2],y(x)\right ]\right \}\]
✓ Maple : cpu = 1.141 (sec), leaf count = 72
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\ln \left ( x \right ) +\int ^{{\it \_Z}}\!-{\frac {1}{{{\it \_a}}^{2}+1} \left ( {\it \_a}\,f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) -\sqrt {- \left ( f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) \right ) ^{2}+f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) } \right ) \left ( f \left ( {\frac {1}{\sqrt {{{\it \_a}}^{2}+1}}} \right ) \right ) ^{-1}}{d{\it \_a}}+{\it \_C1} \right ) x \right \} \]